Question

lmn is an isosceles triangle. what is the approximate length of side lm, and what is the approximate perimeter of triangle lmn? round your answer to the nearest tenth.

a. the approximate length of side lm is 6 units, and the approximate perimeter of triangle lmn is 22.8 units.
b. the approximate length of side lm is 6 units, and the approximate perimeter of triangle lmn is 22 units.
c. the approximate length of side lm is 6.4 units, and the approximate perimeter of triangle lmn is 22.8 units.
d. the approximate length of side lm is 6.4 units, and the approximate perimeter of triangle lmn is 22 units.

Explanation:

Step1: Identify coordinates

Let \(L=(1,1)\), \(M=(5, - 3)\), \(N=(-3,-3)\).

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for \(LM\)

For points \(L(1,1)\) and \(M(5,-3)\), \(x_1 = 1,y_1 = 1,x_2=5,y_2=-3\). Then \(d_{LM}=\sqrt{(5 - 1)^2+(-3 - 1)^2}=\sqrt{4^2+( - 4)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.7\approx6\).

Step3: Find length of \(LN\)

For points \(L(1,1)\) and \(N(-3,-3)\), \(d_{LN}=\sqrt{(-3 - 1)^2+(-3 - 1)^2}=\sqrt{(-4)^2+(-4)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.7\approx6\).

Step4: Find length of \(MN\)

For points \(M(5,-3)\) and \(N(-3,-3)\), \(d_{MN}=\sqrt{(5+3)^2+(-3 + 3)^2}=\sqrt{8^2+0^2}=8\).

Step5: Calculate perimeter \(P\)

\(P=d_{LM}+d_{LN}+d_{MN}\approx6 + 6+8=20\approx22\).

Answer:

B. The approximate length of side LM is 6 units, and the approximate perimeter of triangle LMN is 22 units.